Bifacial concentration on VMJ cell

VMJ cells requires uniform intensity for proper operation. Cells are 9mm x 9mm square and 0.05cm thick. It consist of 40 junctions producing about 23 volts.

The intensity of the light on each junction becomes fairly uniform when the energy at  the front and the back focus are combined at very high concentration level . 50% of the light fall on the front of the cell. The rest is reflected to the back of the cell with a mirror.

The cell will be cooled by immersing it in circulating deionised water in a sealed container. Because of the high voltage, electrolysis of the water will be observed.

Concentration with 395 mm lens

The 395mm square fresnel lens is available as part number BHPA330-2-4 from http://www.bhlens.com/fresnel_lens.aspx 

run 'fresnelx w395 g395 l330 e99.99 s40 r21 c20:4.5 c38:4.5' first to calculate the concentration levels
fresnelx w395 g395 l330 s40 r21 11493.911 2456.038 v.225
 887.65W/m2 refractive index at 589.2nm(1.492) m(20), eff(99.990%) SunHalfAngle(0.26657o)
Total input energy 138 Watts
Acrylic Fresnel Lens Width 395mm x 0.405mm, Area 0.16m2, Focal Length 330mm (f/0.835), 395 grooves
Slice  Radius   Power    Tot   Tot  QEff        Ix      Ax     Area    UV  Blue Green   Red   NIR    IR
                                                                       390   492   622   760  1110  4000
           mm       W      W     %     %                        mm2     %     %     %     %     %     %
   0           138.50    138 100.0  50.8      1.0      1.0   156025   5.6  13.0  19.6  18.2  27.5  16.0
Cell 1 Concentration Level 1493.911x, distance from lens 321.462mm, 0.9741f, nominal radius 5.766mm
   1    0.225    9.43      9   6.8  68.1  66793.5  66793.5     0.16   6.9   3.3   0.0   0.3  73.7  15.7
   2    0.450    8.43     18  12.9  48.3  19914.2  31634.6     0.48   8.0   3.9   0.0   1.0  52.9  34.2
   3    0.675    8.62     26  19.1  44.2  12207.8  20841.5     0.80   8.2   4.2   0.0   1.9  48.8  36.9
   4    0.900    6.38     33  23.7  52.8   6456.5  14548.3     1.11  12.0   6.5   0.0   7.7  53.5  20.3
   5    1.125    5.66     39  27.8  52.8   4457.3  10915.7     1.43  15.1   9.5   0.0  15.6  44.8  15.0
   6    1.350    5.54     44  31.8  50.4   3569.3   8671.0     1.75  17.0  15.7   0.0  24.8  29.9  12.6
   7    1.575    7.70     52  37.4  48.1   4196.3   7483.9     2.07   8.3  33.0   6.0  31.7  10.9  10.0
   8    1.800    9.32     61  44.1  50.7   4401.6   6761.5     2.39   1.8  25.9  14.8  31.0  15.3  11.2
   9    2.025    8.36     69  50.1  51.0   3482.4   6073.3     2.70   1.9  21.4  16.4  32.2  16.2  12.0
  10    2.250    7.72     77  55.7  50.9   2877.3   5466.1     3.02   1.9  19.8  18.4  31.0  16.5  12.3
  11    2.475    7.22     84  60.9  50.8   2436.1   4940.2     3.34   1.9  18.2  20.4  29.9  17.0  12.6
  12    2.700    6.74     91  65.8  50.6   2074.7   4482.5     3.66   1.9  16.9  22.7  28.0  17.4  13.0
  13    2.925    6.27     97  70.3  50.5   1776.0   4082.1     3.98   2.0  15.1  25.2  26.5  17.7  13.5
  14    3.150    5.86    103  74.6  50.2   1536.3   3731.5     4.29   2.0  13.7  28.0  24.4  17.9  14.0
  15    3.375    5.47    109  78.5  49.8   1336.0   3422.7     4.61   2.0  12.3  31.9  21.2  18.0  14.5
  16    3.600    5.14    114  82.2  49.5   1175.1   3150.5     4.93   2.1  10.9  39.3  14.8  18.0  15.0
  17    3.825    4.84    119  85.7  49.7   1038.0   2909.3     5.25   2.1   9.2  40.2  14.7  18.6  15.3
  18    4.050    4.56    123  89.0  49.9    923.6   2694.8     5.57   2.0   8.0  40.4  15.2  19.3  15.2
  19    4.275    4.28    128  92.1  50.4    819.3   2502.6     5.88   2.0   6.6  40.6  15.8  20.2  14.8
  20    4.500    4.03    132  95.0  51.0    731.5   2329.9     6.20   2.1   5.1  41.0  16.4  21.0  14.4
Cell 2 Concentration Level 456.038x, distance from lens 345.453mm, 1.0468f, nominal radius 10.436mm

run 'fresnelx w395 g395 l330 s40 r21 11493.911 29109.688' to calculate the radius and placement of the mirror. 9109.688 = (330 / (330 - (345.453 + 321.462) / 2)) ^ 2 

Tracking Error

Visualisation of tracking error from 0 to 1 degree in step of 0.02 degree.  The image at the top right corner is the reflection of the back of the absorber. The average concentration level over both surfaces is 914 = 395 * 395 * 0.95 / (2 * 9 * 9) 

Concentration with 420 mm lens

The 420mm square fresnel lens is available as part number BHPA330-2-2 from http://www.bhlens.com/fresnel_lens.aspx 

run 'fresnelx w420 g700 l330 e99.99 s40 r21 c20:4.5 c37:4.5' first to calculate the concentration levels
fresnelx w420 g700 l330 s40 r21 11882.951 2367.923 v.225
 887.65W/m2 refractive index at 589.2nm(1.492) m(20), eff(99.990%) SunHalfAngle(0.26657o)
Total input energy 157 Watts
Acrylic Fresnel Lens Width 420mm x 0.248mm, Area 0.18m2, Focal Length 330mm (f/0.786), 700 grooves
Slice  Radius   Power    Tot   Tot  QEff        Ix      Ax     Area    UV  Blue Green   Red   NIR    IR
                                                                       390   492   622   760  1110  4000
           mm       W      W     %     %                        mm2     %     %     %     %     %     %
   0           156.58    157 100.0  50.8      1.0      1.0   176400   5.6  13.0  19.6  18.2  27.5  16.0
Cell 1 Concentration Level 1882.951x, distance from lens 322.395mm, 0.9770f, nominal radius 5.461mm
   1    0.225    9.58     10   6.1  24.4  67827.8  67827.8     0.16   7.4   5.2   0.0   0.0  23.7  63.6
   2    0.450    8.28     18  11.4  38.2  19547.8  31620.0     0.48   8.8   6.3   0.0   0.1  38.3  46.5
   3    0.675    7.04     25  15.9  64.7   9975.9  19596.9     0.80  10.7   8.1   0.0   0.7  66.1  14.4
   4    0.900    6.54     31  20.1  64.5   6617.9  13918.4     1.11  12.1  10.3   0.0   1.4  65.6  10.5
   5    1.125    6.00     37  23.9  59.1   4724.6  10608.4     1.43  13.9  14.5   0.0   2.3  59.3  10.0
   6    1.350    6.51     44  28.1  57.0   4195.2   8649.1     1.75  12.9  20.2   0.0   5.5  53.2   8.2
   7    1.575    9.03     53  33.8  52.3   4917.4   7659.0     2.07   6.6  34.4   6.2  10.8  34.8   7.3
   8    1.800   10.85     64  40.8  53.3   5122.8   7064.6     2.39   1.7  24.9  15.4  18.2  30.3   9.5
   9    2.025    9.71     74  47.0  53.4   4047.2   6431.3     2.70   1.8  21.1  16.3  24.0  26.6  10.1
  10    2.250    8.87     82  52.6  53.0   3306.7   5837.7     3.02   1.9  18.9  17.1  34.0  17.3  10.8
  11    2.475    8.24     91  57.9  52.9   2778.2   5306.7     3.34   1.9  16.6  17.6  36.5  16.2  11.2
  12    2.700    7.69     98  62.8  52.7   2368.9   4837.4     3.66   1.9  14.8  18.7  36.2  16.8  11.6
  13    2.925    7.19    106  67.4  52.5   2037.9   4423.3     3.98   2.0  13.0  20.5  35.3  17.2  12.1
  14    3.150    6.73    112  71.7  52.2   1765.3   4057.2     4.29   2.0  11.4  22.4  34.2  17.5  12.5
  15    3.375    6.32    119  75.7  51.8   1544.3   3733.3     4.61   2.0  10.1  24.4  32.9  17.7  13.0
  16    3.600    5.90    124  79.5  51.5   1347.2   3444.4     4.93   2.1   8.4  26.7  31.2  18.1  13.5
  17    3.825    5.56    130  83.0  51.1   1193.0   3187.3     5.25   2.1   7.1  29.1  29.6  18.2  14.0
  18    4.050    5.23    135  86.4  51.0   1057.5   2957.2     5.57   2.1   5.6  31.7  27.5  18.7  14.4
  19    4.275    4.92    140  89.5  51.1    941.3   2750.6     5.88   2.2   4.1  35.9  23.9  19.4  14.6
  20    4.500    4.65    145  92.5  51.3    845.4   2564.8     6.20   2.2   2.8  43.6  17.0  20.1  14.4
Cell 2 Concentration Level 367.923x, distance from lens 347.204mm, 1.0521f, nominal radius 12.354mm

 

Cost Calculations

Direct Beam Solar irradiation W/m2
Input Aperture

m2

Lens Thickness mm
Optical Transmission/Reflective Efficiency %
Optical Geometric Efficiency %
Cell Efficiency % Concentration Ratio 
Inverter Efficiency %
Daily Sunshine Hours Hours
Equipment Lifetime Years
Interest rate %
Acrylic Resin Cost

$/litre

$ $/kW
Tracking structure Cost $/m2 $ $/kW
Cell Cost $/cm2 $ $/kW
Cost of inverter  $/kW $ $/kW
Balance of system $/kW $ $/kW
Total cost $/m2 $ $/kW
Investment $/kWh/year GWh/year kWh/year
Levelized $/kWh $/hectare/year
Electrical Output kWe Module Efficiency % Thermal Output kWt
Barrel of oil equivalent (578kWhe/Barrel) $/Barrel $/litre
Coal Equivalent (2767kWhe/tonne) tonnes $/tonne tonnes of CO2

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Last updated: 25 June 2010